Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.3 The Product and Quotient Theorems - 8.3 Exercises - Page 369: 7

Answer

$4$

Work Step by Step

Step 1: $[2(\cos135^{\circ}+i\sin135^{\circ})][2(\cos225^{\circ}+i\sin225^{\circ}]$ Step 2: Using the product theorem, the expression becomes $2(2[\cos(135^{\circ}+225^{\circ})+i\sin(135^{\circ}+225^{\circ})]$ Step 3: Simplifying, $4(\cos360^{\circ}+i\sin360^{\circ})$ Step 4: We know that $\cos360^{\circ}=1$ and $\sin360^{\circ}=0$ Step 5: Substituting these values in the expression, $4(1+i(0))$ Step 6: Therefore, the final answer is $4$.
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